Algebraic dynamical systems and Dirichlet's unit theorem on arithmetic varieties
Résumé
In this paper, we study obstructions to the Dirichlet property by two approaches~: density of non-positive points and functionals on adelic $\mathbb R$-divisors. Applied to the algebraic dynamical systems, these results provide examples of nef adelic arithmetic $\mathbb R$-Cartier divisor which does not have the Dirichlet property. We hope the obstructions obtained in the article will give ways toward criteria of the Dirichlet property.
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